IDEAS home Printed from https://ideas.repec.org/a/kap/revdev/v23y2020i1d10.1007_s11147-019-09156-x.html
   My bibliography  Save this article

Conditional risk-neutral density from option prices by local polynomial kernel smoothing with no-arbitrage constraints

Author

Listed:
  • Ana M. Monteiro

    (University of Coimbra)

  • Antonio A. F. Santos

    (University of Coimbra)

Abstract

A new approach is considered to estimate risk-neutral densities (RND) within a kernel regression framework, through local cubic polynomial estimation using intraday data. There is a new strategy for the definition of a criterion function used in nonparametric regression that includes calls, puts, and weights in the optimization problem associated with parameters estimation. No-arbitrage constraints are incorporated into the problem through equality and bound constraints. The approach considered yields directly density functions of interest with minimum requirements needed. Within a simulation framework, it is demonstrated the robustness of proposed procedures. Additionally, RNDs are estimated through option prices associated with two indices, S&P500 and VIX.

Suggested Citation

  • Ana M. Monteiro & Antonio A. F. Santos, 2020. "Conditional risk-neutral density from option prices by local polynomial kernel smoothing with no-arbitrage constraints," Review of Derivatives Research, Springer, vol. 23(1), pages 41-61, April.
    • Handle: RePEc:kap:revdev:v:23:y:2020:i:1:d:10.1007_s11147-019-09156-x
    DOI: 10.1007/s11147-019-09156-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11147-019-09156-x
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11147-019-09156-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
    2. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    3. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    4. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    5. Monteiro, Ana Margarida & Tutuncu, Reha H. & Vicente, Luis N., 2008. "Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity," European Journal of Operational Research, Elsevier, vol. 187(2), pages 525-542, June.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
    8. Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
    9. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    10. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    11. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    12. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.
    13. Yatchew,Adonis, 2003. "Semiparametric Regression for the Applied Econometrician," Cambridge Books, Cambridge University Press, number 9780521812832, September.
    14. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    15. Grith, Maria & Härdle, Wolfgang Karl & Schienle, Melanie, 2010. "Nonparametric estimation of risk-neutral densities," SFB 649 Discussion Papers 2010-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    16. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-672, October.
    17. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints," Journal of Econometrics, Elsevier, vol. 184(2), pages 242-261.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ana M. Monteiro & António A. F. Santos, 2022. "Option prices for risk‐neutral density estimation using nonparametric methods through big data and large‐scale problems," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(1), pages 152-171, January.
    2. Arindam Kundu & Sumit Kumar & Nutan Kumar Tomar, 2019. "Option Implied Risk-Neutral Density Estimation: A Robust and Flexible Method," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 705-728, August.
    3. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    4. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    6. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
    7. Xixuan Han & Boyu Wei & Hailiang Yang, 2018. "Index Options And Volatility Derivatives In A Gaussian Random Field Risk-Neutral Density Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-41, June.
    8. Bo Zhao & Stewart Hodges, 2013. "Parametric modeling of implied smile functions: a generalized SVI model," Review of Derivatives Research, Springer, vol. 16(1), pages 53-77, April.
    9. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    10. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    11. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    12. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    13. Ricardo Crisóstomo, 2021. "Estimating real‐world probabilities: A forward‐looking behavioral framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1797-1823, November.
    14. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.
    15. Dillschneider, Yannick & Maurer, Raimond, 2019. "Functional Ross recovery: Theoretical results and empirical tests," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    16. Grith, Maria & Härdle, Wolfgang Karl & Schienle, Melanie, 2010. "Nonparametric estimation of risk-neutral densities," SFB 649 Discussion Papers 2010-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    17. Marie Brière & Kamal Chancari, 2004. "Perception des risques sur les marchés, construction d'un indice élaboré à partir des smiles d'options et test de stratégies," Revue d'économie politique, Dalloz, vol. 114(4), pages 527-555.
    18. Vladislav Kargin, 2003. "Consistent Estimation of Pricing Kernels from Noisy Price Data," Papers math/0310223, arXiv.org.
    19. repec:hum:wpaper:sfb649dp2010-021 is not listed on IDEAS
    20. Steven Heston & Kris Jacobs & Hyung Joo Kim, 2023. "The Pricing Kernel in Options," Finance and Economics Discussion Series 2023-053, Board of Governors of the Federal Reserve System (U.S.).
    21. Ming Yuan, 2009. "State price density estimation via nonparametric mixtures," Papers 0910.1430, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:revdev:v:23:y:2020:i:1:d:10.1007_s11147-019-09156-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.